Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

Journal of Linear and Topological Algebra

مقاله 4، دوره 03، شماره 01، خرداد 2014، صفحه 23-33   

نویسندگان

R. Ezzati^* ؛ A. Yousefzadeh

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

چکیده

In this paper, we propose the least-squares method for computing the positive solution of a $m\times n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of the non-square FFLS of equations by using pseudoinverse. If 1-cuts vector is non-negative, we solve constrained least squares problem for computing left and right spreads. Then, in the special case, we consider 0 is belong to the support of some elements of coefficient matrix and solve three overdetermined linear systems and if the solutions of these systems held in non-negative fuzzy solutions then we compute the solution of the non-square FFLS of equations. Else, we solve constrained least squares problem for obtaining an approximated non-negative fuzzy solution. Finally, we illustrate the efficiency of the proposed method by solving some numerical examples.

کلیدواژه‌ها

Fuzzy linear system؛ fuzzy number؛ Ranking Function؛ Fuzzy number vector solution

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